Should patients diagnosed with venous thromboembolism and history of brain cancer be treated with anticoagulation or IVC filter placement?

Depends. Anticoagulation can cause bleeding but IVC filters have their own inherent problems including filter thrombosis, postphlebitic syndrome and recurrent DVT/PE.

For patients with brain tumors at increased risk of hemorrhage (ie metastases from melanoma, choriocarcinoma, thyroid carcinoma and renal cell carcinoma) an IVC filter is recommended.

For brain tumors at decreased risk of hemorrhage, anticoagulate for 3 - 6 months, with exception of malignant glioma for which longer term anticoagulation is recommended. While LMWH is more costly, it is preferred over warfarin given decreased interaction with other drugs, convenience of not having to monitor the level of anticoagulation on a regular basis, and greater efficacy at reducing risk of recurrent thromboembolism without increasing risk of bleeding.

Source

Wen, P. MD and Hart, R. MD. "Anticoagulant and antiplatelet therapy in patients with brain tumors." Up to Date. 14 August 2008.